I have received the following answer direct from some of the CASTEP developer group.

' .. external pressure is always specified in Cartesians regardless of cell geometry. Hence hydrostatic P would be

%block external_pressure

GPA

P 0 0

P 0

P

%endblock external_pressure

'

The important point here is that it doesn't matter what the geometry of the unit cell is (i.e. it can have cell angles that are NOT 90 degrees). The external pressure is ALWAYS specified in *orthogonal Cartesian* coordinates.

The explanation you received from the CASTEP developer group indicates that external pressure is defined in Cartesian coordinates regardless of the unit cell geometry. Here’s a detailed and structured clarification based on the provided information:

### Explanation of External Pressure in CASTEP

**Key Points:**

1. **Specification in Cartesian Coordinates:** External pressure in CASTEP is always specified in orthogonal Cartesian coordinates.

2. **Independence from Unit Cell Geometry:** This specification method applies irrespective of the unit cell's geometry, including cases where cell angles deviate from 90 degrees.

3. **Format for Hydrostatic Pressure:** For hydrostatic pressure, the pressure tensor is diagonal with equal elements along the diagonal, which simplifies to:

```plaintext

%block external_pressure

GPA

P 0 0

P 0

P

%endblock external_pressure

```

Here, `P` represents the pressure value in GPa.

### Detailed Breakdown:

1. **Cartesian Coordinates System:**

- The external pressure tensor in CASTEP is defined using an orthogonal Cartesian coordinate system, which is independent of the crystallographic axes of the unit cell.

- This means the pressure components \( P_{xx}, P_{yy}, P_{zz} \) (along with the off-diagonal shear components \( P_{xy}, P_{xz}, P_{yz} \)) are specified in a Cartesian framework.

2. **Application to Any Unit Cell Geometry:**

- The unit cell can have any arbitrary geometry with angles that are not necessarily 90 degrees.

- The use of Cartesian coordinates ensures that the pressure application is consistent and unambiguous regardless of the unit cell's shape and orientation.

3. **Hydrostatic Pressure Example:**

- For applying a hydrostatic pressure \( P \), where the pressure is uniform in all directions, the pressure tensor can be simplified:

```plaintext

%block external_pressure

GPa

P 0 0

P 0

P

%endblock external_pressure

```

- This tensor has the same value \( P \) along the diagonal components, indicating equal pressure in the x, y, and z directions, with zero off-diagonal elements.

### Practical Implications:

- **Consistency:** By using Cartesian coordinates, CASTEP ensures that pressure is applied in a consistent manner, making it easier to interpret and apply pressure conditions across different simulations.

- **Flexibility:** This method allows for straightforward application of various pressure conditions (hydrostatic, uniaxial, etc.) without needing to convert between coordinate systems tailored to specific unit cell geometries.

### Example:

If you wish to apply a hydrostatic pressure of 5 GPa to your system, you would specify it as follows:

```plaintext

%block external_pressure

GPa

5 0 0

5 0

5

%endblock external_pressure

```

This ensures that a uniform pressure of 5 GPa is applied in all directions, irrespective of the unit cell's specific geometry.

In conclusion, the critical takeaway is the invariance of the pressure specification method with respect to the unit cell geometry in CASTEP, always using orthogonal Cartesian coordinates for defining external pressure.